# Graphing Quadratics: putting it all together. 43210 In addition to level 3, students make connections to other content areas and/or contextual situations.

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Graphing Quadratics: putting it all together

Strategies & steps to graphing a quadratic. y = 3x 2 + 2x + 4 1.Determine the vertex. Use x = - b / 2a 1. x = - 2 / 2(3) 2. x = - 1 / 3 3. y = 3(- 1 / 3 ) 2 + 2(- 1 / 3 ) + 4 4. y = 11 / 3 or 3 2 / 3 5. The vertex is (- 1 / 3, 3 2 / 3 ) 2.Use the discriminant to determine the number of solutions. 1.(2) 2 – 4(3)(4) 2.4 – 48 3.-44 4.No real solutions. This means the graph will NOT cross the x-axis.  Factoring or using the quadratic formula will not help you graph this quadratic.  You need to use an “x” point left and right of - 1 / 3 in order to graph this.

Strategies & steps to graphing a quadratic. y = 3x 2 + 2x + 4 3.Point left of and right of - 1 / 3 : (-2, _____) and (1, _____) 1.y = 3(-2) 2 + 2(-2) + 4 2.y = 12 – 4 + 4 3.y = 12 4.(-2, 12) 5.y = 3(1) 2 + 2(1) + 4 6.y = 3 + 2 + 4 7.y = 9 8.(1, 9) 4.Graph the vertex and the two points.

Strategies & steps to graphing a quadratic. y = x 2 + 8x + 16 1.Determine the vertex. Use x = - b / 2a 1. x = - 8 / 2(1) 2. x = -4 3. y = (-4) 2 + 8(-4) + 16 4. y = 0 5. The vertex is (-4, 0) 2.Use the discriminant to determine the number of solutions. 1.(8) 2 – 4(1)(16) 2.64 – 64 3.0 4.One solution. This means the graph will intercept the x-axis at the VERTEX.  Factoring or using the quadratic formula will not help you graph this quadratic. (Your answers will be -4 & -4).  You need to use an “x” point left and right of -4 in order to graph this.

Strategies & steps to graphing a quadratic. y = x 2 + 8x + 16 3.Point left of and right of -4: (-5, _____) and (-3, _____) 1.y = (-5) 2 + 8(-5) + 16 2.y = 25 – 40 + 16 3.y = 1 4.(-5, 1) 5.y = (-3) 2 + 8(-3) + 16 6.y = 9 - 24 + 16 7.y = 1 8.(-3, 1) 4.Graph the vertex and the two points.

Strategies & steps to graphing a quadratic. y = x 2 + 6x + 5 1.Determine the vertex. Use x = - b / 2a 1. x = - 6 / 2(1) 2. x = -3 3. y = (-3) 2 + 6(-3) + 5 4. y = -4 5. The vertex is (-3, -4) 2.Use the discriminant to determine the number of solutions. 1.(6) 2 – 4(1)(5) 2.36 – 20 3.16 4.Two solutions. This means the graph will intercept the x-axis two times.  Factoring or using the quadratic formula will HELP you.  Which one do you want to use?

Strategies & steps to graphing a quadratic. y = x 2 + 6x + 5 3.Factoring will be the quickest way to find the x-intercepts. 1. (x +5)(x + 1) = 0 2. x + 5 = 0 1. x = -5 3. x + 1 = 0 1. x = -1 4.The x-intercepts are (-5, 0) & (-1, 0). 4.Graph the vertex and the x-intercepts.

Strategies & steps to graphing a quadratic. y = -2x 2 + 6x + 1 1.Determine the vertex. Use x = - b / 2a 1. x = - 6 / 2(-2) 2. x = 3 / 2 3. y = -2( 3 / 2 ) 2 + 6( 3 / 2 ) + 1 4. y = -2( 9 / 4 ) + 9 + 1 5. The vertex is (1½, 5 ½ ) 2.Use the discriminant to determine the number of solutions. 1.(6) 2 – 4(-2)(1) 2.36 + 8 3.44 4.Two solutions. This means the graph will intercept the x-axis two times.  Because 44 is not a perfect square, the x-intercepts will be irrational.  Use the quadratic formula to find the x- intercepts.

Strategies & steps to graphing a quadratic. y = -2x 2 + 6x + 1 3.Substitute into the quadratic formula and solve to find your x- intercepts. 4.Divide 6, 2 and 4 by 2 (the GCF).

Strategies & steps to graphing a quadratic. y = -2x 2 + 6x + 1 5.Estimate the value of the irrational x-intercepts. 6.Graph the vertex and the x-intercepts.

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